Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials

We extend a result of Davies and Nath on the location of eigenvalues of Schr\"odinger operators with slowly decaying complex-valued potentials to higher dimensions. In this context, we also discuss various examples related to the Laptev--Safronov conjecture.Comment: Some typos correcte

Spectral theory of a mathematical model in Quantum Field Theory for any spin

In this paper we use the formalism of S.Weinberg in order to construct a mathematical model based on the weak decay of hadrons and nuclei. In particular we consider a model which generalizes the weak decay of the nucleus of the cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock space. The Hamiltonian is self-adjoint and has an unique ground state. By using the commutator theory we get a limiting absorption principle from which we deduce that the spectrum of the Hamiltonian is absolutely continuous above the energy of the ground state and below the first threshold.Comment: A subsection revise

Bounds on primitives of differential forms and cofilling inequalities

We prove that on a Riemannian manifold, a smooth differential form has a primitive with a given (functional) upper bound provided the necessary weighted isoperimetric inequalities implied by Stokes are satisfied. We apply this to prove a comparison predicted by Gromov between the cofilling function and the filling area.Comment: The new features of the main result are its sharpness and the fact that the manifold is not assumed have bounded geometry, nor even to be complete. This paper corresponds to a part of a talk given in January 2004 in Haifa, at a workshop in memory of Robert Brooks. The other part, which is the "translation" in the framework of geometric group theory, will soon be deposited on arxi

Dual elliptic structures on CP2

We consider an almost complex structure J on CP2, or more generally an elliptic structure E which is tamed by the standard symplectic structure. An E-curve is a surface tangent to E (this generalizes the notion of J(holomorphic)-curve), and an E-line is an E-curve of degree 1. We prove that the space of E-lines is again a CP2 with a tame elliptic structure E^*, and that each E-curve has an associated dual E^*-curve. This implies that the E-curves, and in particular the J-curves, satisfy the Pl\"ucker formulas, which restricts their possible sets of singularities.Comment: 18 pages The only difference with the first version is the mention of the thesis of Benjamin MacKay ("Duality and integrable systems of pseudoholomorphic curves", Duke University, 1999), which I did not know at the time, and which contains a large part of the results of my pape

Geometric descriptions of polygon and chain spaces

We give a few simple methods to geometically describe some polygon and chain-spaces in R^d. They are strong enough to give tables of m-gons and m-chains when m <= 6